A bar of silicon is doped with boron concentration of $10^{16} \text{cm}^{-3}$ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of $10^{20} \text{cm}^{-3} s^{-1}$. If the recombination lifetime is $100 \;\mu s$, intrinsic carrier concentration of silicon is $10^{10} \text{cm}^{-3}$ and assuming $100\%$ ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is
- $10^{20} \text{cm}^{-6}$
- $2 \times 10^{20} \text{cm}^{-6}$
- $10^{32} \text{cm}^{-6}$
- $2 \times 10^{32} \text{cm}^{-6}$